LCM of 3 Numbers Calculator LCM of 4 Numbers Calculator LCM of 5 Numbers Calculator LCD Calculator How to find LCM LCM and HCF Questions Least Common Denominator Calculator Greatest Common Divisor Calculator HCF Calculator HCF of 3 Numbers Calculator HCF of 4 Numbers Calculator GCD Calculator Greatest Common Factor Calculator Least Common Multiple Calculator Common Factors Calculator

GCF of 213/58, 678/565

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 213/58, 678/565 i.e 3/32770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/58, 678/565.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 213/58,678/565?

Given fractions are 213/58,678/565

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 213/58,678/565, numerators are 213,678

Denominators are 58,565

The GCF of 213,678 is 3 .

LCM of 58,565 is 32770.

The greatest common factor of 213/58,678/565 = [GCF of 213,678]/[LCM of 58,565]= 3/32770

Therefore, the GCF of 213/58,678/565 is 3/32770.

Greatest Common Factor of 213,678

To find the highest common factor of 213,678, we have to find the factors of both numbers and list the highest common factor.

The factors of 213 are 1, 3, 71, 213

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The HCF of 213,678 is 3.

Lets's calculate GCF of 213,678

Greatest Common Factor (GCF) of 213,678 By Common Division

3 213, 678
71, 226

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 213,678 By Matching Biggest Common Factor Method

Greatest Common Factor of 213,678 By Matching Biggest Common Factor Method

Now, list down the factors of 213

:

1,3,71,213

Now, list down the factors of 678

:

1,2,3,6,113,226,339,678

Greatest Common Factor

We found the factors 213,678 . The biggest common factor number is the GCF number.
So the greatest common factor 213,678 is 3.

Lets's calculate LCM of 58,565

Lowest Common Multiple of 58,565 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 32770

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/32770

Therefore, the GCF of Fractions 213/58,678/565 is 3/32770

Least Common Multiple of 58,565 with GCF Formula

Least Common Multiple of 58,565 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 58,565 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(58,565) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(58,565) x common factors =1 x 1 = 1

LCM(58,565) = ( 58 × 565 ) / 1

LCM(58,565) = 32770 / 1

LCM(58,565) = 32770


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 213/58, 678/565

1. What is the HCF of 213,678?

The HCF of 213,678 is 3

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 213/58, 678/565?

Answer: GCF of Numerators as per given numbers 213/58, 678/565 is

GCF of Numerators i.e. for 213,678 is 3

LCM of denominators i.e. for 58,565 is 32770.

Thus, GCF of Fractions is 3/32770.Finally, GCF of Fractions for 213/58, 678/565 is 3/32770.